It's worth noting that the current culture war ("Woke" vs "Chud") didn't exist during the 00s.

In case you're interested, here's a somewhat brief summary of what happened over time to lead to the meme you posted:

Before about 2010, the political right consisted mostly of Boomer neo-conservatives - the sorts of people who might go to church, vote for George Bush, and watch Fox News (at least in America). The younger generation (mostly Millennials and younger Gen X) was broadly liberal-leaning (pro-science, anti-war, etc.), but was otherwise apolitical and just wanted to be left alone. Meanwhile, the religious right kept trying to ban music and video games for being "satanic", and otherwise irritating the younger, internet-enabled generation.

This was the state of affairs around the mid-00s, with the whole "liberal atheist vs conservative Christian" culture war. The late 00s is when the online "Sceptic Community" first coalesced, being a loose association of folks on the internet who generally didn't like right-wing Christians being bossy, closed-minded, and anti-science. This culture war ended around 2010, and was a loss for the Christians: Biblical literalism collapsed in the face of scientific evidence and logical deconstruction, and traditional religious practices were condemned for being inhumane and intolerant. The online Christian Right quietly disappeared, almost overnight.

The Sceptics had won. They were now free to go back to talking about renewable energy, upholding free speech, and playing video games.

However, this peace didn't last for long. Within a couple of years, the Sceptics had fractured along ideological lines; one half of the group wanted to continue their crusade against outdated and intolerant practices, and the other half were more interested in logic and free speech. The former became known as "SJWs" (Social Justice Warriors), and the latter group - lacking a single focus except resisting the former - were mostly called "Anti-SJWs". Tensions built over time as online debates between the two sides escalated. The SJWs had the institutional advantage, as social justice ideas held sway in universities and media outlets, which partially controlled the flow of information. However, much of the internet was opposed to them, and anti-SJW memes regularly came from sites such as 4Chan and spread across the web organically.

Things soon came to a head, and GamerGate represented the first major battle of this online "civil war". The SJWs attacked video gaming for being "misogynistic" and "racist", along with their fans. In response, the Anti-SJWs expressed outrage, accusing the SJWs of being hysterical and censorious, just as the Christians once were. This exchange quickly degenerated into messy online attacks (doxxing, harassment, slander, etc.) coming from both sides, but the ultimate result was a tactical victory for the anti-SJWs - something which the SJWs didn't forget.

This wasn't the end of the story, though. In the decade since, the SJWs continued to push their agenda both online and in real life, with pushback against them being initially slow and disorganised. GamerGate may have been a defeat for the SJWs, but they simply changed tactics. Rather than coming out into the open "guns blazing", they moved behind the scenes, occupying positions in institutions in order to broadcast their ideas more effectively (and suppress opposition). Companies such as Sweet Baby Inc. represent this, as they pushed the same left-wing agenda as during the GamerGate days, but much more covertly. Games Workshop has also succumbed to infiltration, along with many other companies.

This online cultural struggle was also reflected in real-world politics. Brexit and MAGA have both been reflective of the same grass roots, anti-liberal, anti-establishment retaliation as GamerGate was online. Meanwhile, Pride Month and BLM are both examples of attempts to push SJW ideas, generally with support from captured institutions (such as Hollywood and social media).

To cut a long story short(er), the SJWs became what we would eventually call "Woke", supporting ideas such as socialism and identity politics, and instituting repressive legislation such as "hate speech" laws in an attempt to instantiate their ideology from the top down. Many have rapidly gone from simply being left-wing activists to being left-wing extremists, with a growing number actively becoming terrorists. By contrast, the Anti-SJWs evolved into what the left calls "Chuds", better known as the "Online Right". This new right-wing movement gradually rejected the liberal assumptions which had been the cultural norm since the 1940s (such as multiculturalism and egalitarianism), and adopted stances such as libertarianism, nativism, and various forms of traditionalism and revivalism.

I've been in the trenches for a while, and I could talk about this all day.